John Monaghan is a professor at the University of Agder, Norway and an emeritus professor at the University of Leeds, UK. He has taught in schools and universities, and the learning and teaching of calculus has been a research interest throughout his career.Robert Ely is a professor of mathematics education at the University of Idaho, United States. He studies the reasoning of students with infinitesimals, integrals, variables, and argumentation, and he is particularly interested in the perspectives that history can bring to such reasoning.Márcia M.F. Pinto is Associate Professor at a public university in Brazil. She has experience teaching mathematics to prospective teachers, mathematicians and engineers and co-authoring textbooks for distance learning courses on calculus.Mike Thomas is Professor Emeritus in the Mathematics Department at Auckland University, New Zealand. His research explores advanced mathematical thinking at school and university, including the role of representations, versatility and digital technology.

Back cover quotes:‘I highly recommend this book. You will undoubtably be inspired and awed at the beauty of the ideas presented.’ Chris Rasmussen‘The most impressive aspect of this book is that the authors cover so much ground without taking a stance on any of the controversies they so carefully explain.’ Pat Thompson‘When we teach calculus, we need to know about differential and infinitesimal ways to understand calculus … how calculus ideas evolved over time … calculus curricula around the world … calculus education research … alternatives to the classic order … calculus in solving real-world problems … [this book] does quite a bit of all of that.’ Elena Nardi

• Series foreword1 – Introduction2 – Calculus across time and over countries3 – Making sense of limits and continuity4 – Making sense of differentiation5 – Integration and the fundamental theorem of calculus6 – Interlude: The ordering of chapters 3, 4 and 57 – Calculus applications: differential equations and integration8 – Beyond elementary calculusIndex

John Monaghan is a professor at the University of Agder, Norway and an emeritus professor at the University of Leeds, UK. He has taught in schools and universities, and the learning and teaching of calculus has been a research interest throughout his career.Robert Ely is a professor of mathematics education at the University of Idaho, United States. He studies the reasoning of students with infinitesimals, integrals, variables, and argumentation, and he is particularly interested in the perspectives that history can bring to such reasoning.Márcia M.F. Pinto is Associate Professor at a public university in Brazil. She has experience teaching mathematics to prospective teachers, mathematicians and engineers and co-authoring textbooks for distance learning courses on calculus.Mike Thomas is Professor Emeritus in the Mathematics Department at Auckland University, New Zealand. His research explores advanced mathematical thinking at school and university, including the role of representations, versatility and digital technology.

Back cover quotes:‘I highly recommend this book. You will undoubtably be inspired and awed at the beauty of the ideas presented.’ Chris Rasmussen‘The most impressive aspect of this book is that the authors cover so much ground without taking a stance on any of the controversies they so carefully explain.’ Pat Thompson‘When we teach calculus, we need to know about differential and infinitesimal ways to understand calculus … how calculus ideas evolved over time … calculus curricula around the world … calculus education research … alternatives to the classic order … calculus in solving real-world problems … [this book] does quite a bit of all of that.’ Elena Nardi

• Series foreword1 – Introduction2 – Calculus across time and over countries3 – Making sense of limits and continuity4 – Making sense of differentiation5 – Integration and the fundamental theorem of calculus6 – Interlude: The ordering of chapters 3, 4 and 57 – Calculus applications: differential equations and integration8 – Beyond elementary calculusIndex

John Monaghan is a professor at the University of Agder, Norway and an emeritus professor at the University of Leeds, UK. He has taught in schools and universities, and the learning and teaching of calculus has been a research interest throughout his career.Robert Ely is a professor of mathematics education at the University of Idaho, United States. He studies the reasoning of students with infinitesimals, integrals, variables, and argumentation, and he is particularly interested in the perspectives that history can bring to such reasoning.Márcia M.F. Pinto is Associate Professor at a public university in Brazil. She has experience teaching mathematics to prospective teachers, mathematicians and engineers and co-authoring textbooks for distance learning courses on calculus.Mike Thomas is Professor Emeritus in the Mathematics Department at Auckland University, New Zealand. His research explores advanced mathematical thinking at school and university, including the role of representations, versatility and digital technology.

Back cover quotes:‘I highly recommend this book. You will undoubtably be inspired and awed at the beauty of the ideas presented.’ Chris Rasmussen‘The most impressive aspect of this book is that the authors cover so much ground without taking a stance on any of the controversies they so carefully explain.’ Pat Thompson‘When we teach calculus, we need to know about differential and infinitesimal ways to understand calculus … how calculus ideas evolved over time … calculus curricula around the world … calculus education research … alternatives to the classic order … calculus in solving real-world problems … [this book] does quite a bit of all of that.’ Elena Nardi

• Series foreword1 – Introduction2 – Calculus across time and over countries3 – Making sense of limits and continuity4 – Making sense of differentiation5 – Integration and the fundamental theorem of calculus6 – Interlude: The ordering of chapters 3, 4 and 57 – Calculus applications: differential equations and integration8 – Beyond elementary calculusIndex